'They made you feel good' … the Beatles and George Martin pick up a silver disc in 1963 Photograph: Chris Ware/Getty

'This was the year in which I had 37 weeks at No 1," says George Martin in the new BBC Arena documentary, Produced By George Martin. He's talking about 1963, the year the Beatles broke through. While the exact number of weeks remains in dispute – thanks to the still vexed question of whether Please Please Me went to No 1 – this achievement has never been bettered.

Often overlooked in pop histories, 1963 saw a revolution. Between 11 April and 31 December, George Martin productions – singles by Gerry and the Pacemakers, Billy J Kramer and the Dakotas, and the Beatles – monopolised the top of the charts. The picture is even more complete when you factor in the album charts. After 11 May, while the Beatles were at No 1 with From Me to You, their two albums, Please Please Me and With the Beatles, remained at the top for the following 51 weeks. They supplanted Cliff Richard's Summer Holiday – No 1 for 14 weeks in early 1963 – and thereby lies a story.

In Francis Hanly's Arena film, Martin freely admits to his competitiveness. Back in 1962, the man to beat was Norrie Paramor, who, as recording director for EMI's Columbia records, had bossed British pop since the late 50s. Now an unjustly forgotten figure, Paramor nurtured Cliff and built an empire on his productions for the Shadows, Helen Shapiro and Frank Ifield.

At the comparatively lowly EMI label Parlophone, Martin seethed as Paramor racked up 26 weeks at No 1 during 1962. "He drove an E-Type Jag," Martin remembers. "It didn't matter what they recorded, it could have been God Save the Queen, [but it] became No 1. I envied that."

Martin's break came from a most unlikely source. On 13 February 1962, he met Brian Epstein, manager of a group from Liverpool – way out in the sticks as far as the music industry was concerned. Epstein had already been rejected by several record companies and was nearing the point of desperation.

Martin also turned the Beatles down. But, as he recalls, Epstein "was so disappointed that I gave him a lifeline – 'I'll give them an hour in the studio, OK?'" When they eventually arrived, "they had this wonderful charisma: they made you feel good".

The Beatles' first Parlophone single, Love Me Do, made the top 20. Martin then wanted them to record a catchy potboiler, Mitch Murray's How Do You Do It. They complied reluctantly. Martin next went with the group's choice, Please Please Me, which went to No 1 in February 1963 in all charts but that of Record Retailer, the one used by the Guinness Book of Records.

The race was on, and the relationship between producer, manager and group set. Martin was flexible enough to trust the Beatles' instincts. Unlike, say, Norrie Paramor, he worked with them, using his well-honed musical and arranging skills to enhance their records. He suggested that Please Please Me be speeded up, and that the song begin with the chorus.

In retrospect, Epstein and Martin grounded the four talented but piratical young men: they made the Beatles palatable enough to the variety-dominated showbiz establishment of the day, while giving them artistic freedom. This was a breakthrough in the artist-producer relationship, and paved the way for the Rolling Stones and the liberation of mid-60s pop.

Epstein was so pleased with Martin that he brought his other artists to Parlophone: Billy J Kramer, Gerry and the Pacemakers and Cilla Black. The combination worked to unforeseen effect during 1963, as the Liverpool beat-group sound swept the nation. Suddenly, the string-laden, almost light-entertainment sound of Paramor pop began to seem passe.

Martin hardly registered his success. "My workload was enormous," he says, "and I had such little time." But it wasn't as though the explosion happened overnight: the Beatles had been going for nearly six years, while Brian Epstein had his first breakthrough after 28 years of false starts. Martin, too, had been in the business for more than a decade.

One of the delights of Hanly's film is the way it traces the producer's life: from his upbringing in north London to service in the Fleet Air Arm, to his joining EMI, in 1950, as assistant to Parlophone head Oscar Preuss.

Martin found his groove with a sequence of brilliant comedy records by the Goons, Flanders and Swann, and the cast of Beyond the Fringe. As he puts it, they were "sound pictures" – the studio used as an instrument to "make people imagine that they were there".

But the Beatles were unprecedented, and, as 1963 went on, the mania built. You can hear it in the records as they escalate in confidence and intensity: From Me to You is still teen pop, but She Loves You is incandescent. Sophisticated yet ecstatic, tricksy yet, on occasion, pulverising, With the Beatles defined the pop album.

The question remains: why did this happen in 1963? Some of it is to do with a natural pop cycle. Although Cliff Richard was almost exactly the same age as John Lennon, he had been having hits since 1958 and was thoroughly integrated into showbiz. A younger generation – coinciding with the demographic surge of the postwar baby boom – wanted something of their own.

Existentialism went pop, and its agents ended 1963 at the peak of their British fame. By mid-December, the Beatles were totally imperial: Fleet Street regulars, national heroes, with gold and silver discs falling like confetti. Their fourth 1963 single, I Want to Hold Your Hand, was the summation of that year: an impossibly (for then) complex record, almost three songs in one, with spectacular changes between verse, chorus and the climactic tag-line "I can't hide" – so explosively transcendent that Bob Dylan misheard it as "I get high".

But the year wasn't quite over yet. On 27 December, Capitol Records rush-released I Want to Hold Your Hand as the group's first US single. Exemplars of the new Britain, the Beatles would soon be claimed by the world. Nineteen sixty-three might have seemed like a culmination, but it was only the beginning.